Problem: Multiply and simplify the following complex numbers: $({3-4i}) \cdot ({-3+2i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({3-4i}) \cdot ({-3+2i}) = $ $ ({3} \cdot {-3}) + ({3} \cdot {2i}) + ({-4i} \cdot {-3}) + ({-4i} \cdot {2i}) $ Then simplify the terms: $ (-9) + (6i) + (12i) + (-8i^2) $ Imaginary unit multiples can be grouped together. $ -9 + (6 + 12)i - 8 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -9 + (6 + 12)i - (-8) $ The result is simplified: $ (-9 + 8) + (18i) = -1+18i $